Explicit bounds for linear difference equations /
This thesis provides explicit, applicable bounds for solutions of a wide class of
second-order difference equations with nonconstant coefficients. Among the applications
is an affirmative answer to a question of Stevi?. We also present bounds for
second-order difference equations with positive restricted (nonconstant) coefficients.
It is determined that whenever the coefficients of the associated monic equation are
less than the constant (1/3)1/3, all solutions tend to zero at an exponential rate. This
constant is optimal. Some further asymptotic results and optimal explicit inequalities
are also given. We then extend our results to give explicit, applicable bounds for solutions
of a wide class of third-order difference equations with nonconstant coefficients.
The techniques used are readily adaptable for higher order equations.
School:Wake Forest University
School Location:USA - North Carolina
Source Type:Master's Thesis
Date of Publication: